That said, in those cities they are far from absurd. I started out similar to you (coding since elementary school) and now live in NYC ~3.5 years out of college. Off the top of my head, I could name half a dozen developers making seven figures, and at least 100 making over $200k.
I'm shocked you know the salaries of 100 other developers. Care to share some of the companies that are paying this much to developers 3.5 years out of college? I'd love to corroborate on glassdoor.
I recently turned down an offer from Google for $270k total comp, so they're definitely one of the high-paying companies. I know Facebook pays similarly well, but have no interest in working there. Being in NYC, though, the highest paying are mostly in finance.
I've found Glassdoor to run very low for higher-paying positions, though. Their numbers are all salary as far as I can tell, while a large portion of compensation is in RSUs and bonuses (40%-90% at compensation levels of $250k and up).
I'm a natural (coding since 3rd grade), out of college for 6 years, and I've only known 1 engineer in my career who made over 200k. Now if by BigCo you mean Facebook, Google, Apple, Amazon, then I don't know them, so I can't comment.
But if by BigCo you mean IBM, Cisco, Intel, etc then I can guarantee you that I don't know a single person making 250k, and glassdoor generally corroborates (if you google STAFF (> senior) software engineer in SF for IBM your average is 132 base in SF)